please explain the method followed in solving such cases where the exponent is a negative number..

thanks

You are looking for a number x such that (mod 100)

Basically we're down to trial and error, but we can make the following observation: since the base is 100 we can simply start looking at numbers that multiply by 7 to end in a 1. So we start with this list:
3, 13, 23, 33, 43, 53, 63, 73, 83, 93

We also know that in the integer system x is going to have to be larger than 6 to make 17x > 100, so we can count out the 3. (Small savings, but in other problems it might cut the list down significantly.)

plz explain the method followed in solving such cases where the exponent is a negative number..

It means the inverse of a number. Given a positive interger and any integer , we can write (modulo )) iff . Exactly what topsquak said. It is the inverse.
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We want to find such that:.
Since .
We can simulatenously solve (since ) the congruences: